1. Field
The present application relates to an image processing method, a carrier medium carrying an image processing program, an image processing apparatus, and an imaging apparatus for performing geometric transformation processing on a shot image by an optical system.
2. Description of the Related Art
Shooting lenses of general cameras are designed so that an image that is similar to a subject plane assumed is formed on an imaging plane. Therefore, when attention is paid to a subject existing at a local position in a shot image, the magnification in the radial direction (i.e., the direction from the optical axis center toward the image periphery) is larger than that in the circumferential direction (i.e., the direction around the optical axis center). In this specification, in the following, the discrepancy between the radial magnification and the circumferential magnification of a subject existing at a local position in an image will be called “magnification distortion.”
Unlike the distortion aberration, the magnification aberration occurs even if a shooting lens is free of aberrations. And the magnification aberration corresponds to differences in impressions between a subject as observed by the naked eyes and its shot image through a shooting lens. For example, when an observer gazes at a subject that is not located at the center when observing a relatively wide field with the naked eyes, the axes of sighting of the eyeballs of the observer are inclined without the observer's realizing it. On the other hand, the optical axis is fixed when the same field is shot through a shooting lens. Therefore, in a shot image through the shooting lens, a subject that is located at a peripheral position looks thicker in the radial direction. This is magnification distortion and is more remarkable as the position goes outward in a wide-angle image.
The geometric transformation characteristic of a projection algorithm that is free of distortion aberration, that is, a projection algorithm that is high in line reproducibility, is given by the following Inequality (A), where h is the image height and θ is the subject angle. This geometric transformation characteristic causes magnification distortion though it is high in line reproducibility.h(θ)∝ tan θ  (A)
On the other hand, among projection algorithms of fish-eye lenses etc. is a stereographic projection algorithm that does not cause magnification distortion. The geometric transformation characteristic of the stereographic projection algorithm is given by the following Inequality, where h is the image height and θ is the subject angle. This geometric transformation characteristic is low in line reproducibility though it does not cause magnification distortion.h(θ)∝ tan(θ/2)  (B)
In view of the above, a geometric characteristic that lies midway between Inequalities (A) and (B) is proposed in Patent Document 1 (Japanese Unexamined Patent Application Publication No. 2005-110207). This in-between geometric characteristic is given by the following Inequality (C). In Inequality (C), P is a predetermined value that satisfies a relationship 1<P<4.h(θ)∝ tan(θ/P)  (C)
Conventionally, it has been considered that both of magnification distortion reduction and high reproducibility can be attained by performing geometric transformation processing on a shot image by a camera according to this geometric transformation characteristic.
However, the geometric transformation characteristic of Inequality (C) does not always make it possible to express the entire area of an image satisfactorily and noticeable line distortion or magnification distortion may occur depending on the position in an image.